There is a class of instruments that measures the coordinates of a point by sending a laser beam to a retroreflector target in contact with the point. The instrument determines the coordinates of the point by measuring the distance and the two angles to the target. The distance is measured with a distance-measuring device such as an absolute distance meter or an interferometer. The angles are measured with an angle-measuring device such as an angular encoder. A gimbaled beam-steering mechanism within the instrument directs the laser beam to the point of interest.
The laser tracker is a particular type of coordinate-measuring device that tracks the retroreflector target with one or more laser beams it emits. There is another category of instruments known as total stations or tachymeters that may measure a retroreflector or a point on a diffusely scattering surface. Laser trackers, which typically have accuracies on the order of a thousand of an inch and as good as one or two micrometers under certain circumstances, are usually much more accurate than total stations. The broad definition of laser tracker, which includes total stations, is used throughout this application.
Ordinarily the laser tracker sends a laser beam to a retroreflector target. A common type of retroreflector target is the spherically mounted retroreflector (SMR), which includes a cube-corner retroreflector embedded within a metal sphere. The cube-corner retroreflector includes three mutually perpendicular mirrors. The vertex, which is the common point of intersection of the three mirrors, is located near the center of the sphere. Because of this placement of the cube corner within the sphere, the perpendicular distance from the vertex to any surface on which the SMR rests remains nearly constant, even as the SMR is rotated. Consequently, the laser tracker can measure the 3D coordinates of a surface by following the position of an SMR as it is moved over the surface. Stating this another way, the laser tracker needs to measure only three degrees of freedom (one radial distance and two angles) to fully characterize the 3D coordinates of a surface.
Some laser trackers have the ability to measure six degrees of freedom (DOF), which may include three translations, such as x, y, and z, and three rotations, such as pitch, roll, and yaw. An exemplary six-DOF laser tracker system is described in U.S. Pat. No. 7,800,758 ('758) to Bridges, et al., incorporated by reference herein. The '758 patent discloses a probe that holds a cube corner retroreflector, onto which marks have been placed. The cube corner retroreflector is illuminated by a laser beam from the laser tracker, and the marks on the cube corner retroreflector are captured by an orientation camera within the laser tracker. The three orientational degrees of freedom, for example, the pitch, roll and yaw angles, are calculated based on the image obtained by the orientation camera. The laser tracker measures a distance and two angles to the vertex of the cube-corner retroreflector. When the distance and two angles, which give three translational degrees of freedom of the vertex, are combined with the three orientational degrees of freedom obtained from the orientation camera image, the position of a probe tip, arranged at a prescribed position relative to the vertex of the cube corner retroreflector, can be found. Such a probe tip may be used, for example, to measure the coordinates of a “hidden” feature that is out of the line of sight of the laser beam from the laser tracker.
As explained hereinabove, the vertex of a cube corner retroreflector within an SMR is ideally placed at the exact center of the sphere into which the cube corner is embedded. In practice, the position of the vertex is off the center of the sphere by up to a few thousandths of an inch. In many cases, the difference in the positions of the vertex and the sphere center are known to high accuracy, but this data is not used to correct the tracker readings because the orientation of the SMR is not known. In the accurate measurements made with laser trackers, this error in the centering of the cube corner retroreflector in the sphere is sometimes larger than the errors from the distance and angle meters within the laser tracker. Consequently, there is a need for a method to correct this centering error.
Most of the SMRs in use today contain open-air cube corner retroreflectors. There are some SMRs that use glass cube corner retroreflectors, but these have limited accuracy. Because of the bending of the light entering such glass cube corners, the light appears to travel in a direction that is not the true direction within the cube corner. The error this produces can be minimized by moving the vertex of the cube corner behind the center of the sphere. An example of the calculations involved in minimizing this error is given in U.S. Pat. No. 7,388,654 to Raab, et al., the contents of which are incorporated by reference. However, there is no one distance of movement that eliminates the tracker errors in using such a retroreflector over the full range of angles of incidence over which light can enter the cube corner. As a result, SMRs made with glass cube corners tend to be made very small, as this reduces error, and they tend to be used in applications where the highest accuracy is not required. However, SMRs made with glass cube corners have a significant advantage compared to SMRs made with open-air cube corners: they have a wider acceptance angle. In other words, the light may enter a glass cube corner at a larger angle of incidence without being clipped than an open-air cube corner. Consequently, there is a need for a method of measuring a relatively large SMR containing a glass cube corner with high accuracy. The need is essentially one of finding the center of the SMR spherical surface, regardless of the position of the glass cube corner, and in this respect it is similar to the need described above for SMRs containing open-air cube corners.
More generally, there is a need for a method of finding the center of a target having a spherical surface and containing a retroreflector, regardless of the type of retroreflector. For example, a different type of retroreflector put into spherical surfaces is the cateye retroreflector. Another example is the photogrammetric dot—a small circle of reflective material—which is sometimes centered in a sphere. There are errors in the centering of cateye retroreflectors and photogrammetric dots in spheres, just as in centering cube corner retroreflectors in spheres. Hence there is a general need for a method of finding the center of a target having a spherical surface and containing a retroreflector.